Duplicate rotate vertices around obect origin?
There are 2 aspects to the definition of the rotation: its Orientation (the direction of the axis of rotation), and its Pivot (the location of the axis of rotation).
In the illustrated Adjust Last Operation panel, you are being offered only the Orientation. If you set the working Pivot to '3D Cursor' in the header, and, in Object mode, with your object selected, ShiftS &gt; Cursor to Selected, the pivot should be on the object origin ('the orange dot'), and you should be good to go.
(You can bring up the Pivot options by hitting keyboard  . (period).)
This assumes one of the Orientation options you are being offered is OK. If it isn't, you may have to create a Custom Orientation for the rotation by checking the little '+' in the Header &gt; Transform Orientation dropdown.
And here, there seems to be a bug in my recent 2.91. The panel does not offer you your Custom Orientation, along with the others.
It still works.. supposing I set my orientation from a face, then  Shift D R Z, the orientation will still be normal to the face, and  Shift D R Z Z will still revert to Global orientation.